Chapter 11

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 4+2+1+\ldots $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ -1,-6,-36,-216, \dots $$

Find the 32nd term of each sequence. \(34,37,40,43, \ldots\)

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ y=-x^{2}+4 $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 1+2+4+\ldots $$

Is the sequence geometric? If so, find the common ratio and the next two terms. $$ \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \ldots $$

Find the 32nd term of each sequence. \(-9,-8.7,-8.4, \dots\)

Write a recursive formula for each sequence. Then find the next term. $$ -2,-1,0,1,2, \ldots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ y=\frac{2}{3} x^{2}+5 $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 6+18+54+\ldots $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ 2+4+6+\ldots ; n=4 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=5, r=-3 $$

Find the 32nd term of each sequence. \(0.1,0.5,0.9,1.3, \dots\)

Write a recursive formula for each sequence. Then find the next term. $$ 43,41,39,37,35, \ldots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ h(x)=5 x^{2} $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ -54-18-6-\dots $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ 8+9+10+\ldots ; n=8 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=0.0237, r=10 $$

Find the 32nd term of each sequence. \(0.0023,0.0025,0.0027, \ldots\)

Write a recursive formula for each sequence. Then find the next term. $$ 40,20,10,5, \frac{5}{2}, \dots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ y=4-\frac{1}{4} x^{2} $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 1-1+1-\ldots $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ 5+6+7+\ldots ; n=7 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=\frac{1}{2}, r=\frac{2}{3} $$

Find the 32nd term of each sequence. \(101,105,109,113, \ldots\)

Write a recursive formula for each sequence. Then find the next term. $$ 6,1,-4,-9, \dots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ h(x)=-(x-2)^{2}+5 $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ 1+\frac{1}{5}+\frac{1}{25}+\ldots $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ 1+4+7+10+\ldots ; n=11 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=1, r=0.5 $$

Find the 32nd term of each sequence. \(213,201,189,177, \ldots\)

Write a recursive formula for each sequence. Then find the next term. $$ 144,36,9, \frac{9}{4}, \dots $$

Write and evaluate a sum to estimate the area under each curve for the domain \(0 \leq x \leq 2\) . a. Use inscribed rectangles 1 unit wide. b. Use eircumscribed rectangles 1 unit wide. $$ y=(x-2)^{2}+2 $$

Decide whether each infinite geometric series diverges or converges. State whether each series has a sum. $$ \frac{1}{4}+\frac{1}{2}+1+2+\ldots $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ 7+14+21+\ldots ; n=15 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=100, r=-20 $$

Find the 32nd term of each sequence. \(3,1,-1,-3, \dots\)

Write a recursive formula for each sequence. Then find the next term. $$ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ y=-x^{2}+2 $$

Evaluate the finite series for the specified number of terms. $$ 4+12+36+\ldots ; n=6 $$

Use summation notation to write each arithmetic series for the specified number of terms. $$ (-3)+(-6)+(-9)+\ldots ; n=5 $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=7, r=1 $$

Find the 32nd term of each sequence. \(23,30,37,44, \dots\)

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ 4,5,6,7,8, \dots $$

Find the area under each curve for the domain \(0 \leq x \leq 1\) $$ f(x)=x+2 $$

Evaluate the finite series for the specified number of terms. $$ 1+2+4+\ldots ; n=8 $$

For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. $$ \sum_{n=1}^{5}(2 n-1) $$

Write the explicit formula for each sequence. Then generate the first five terms. $$ a_{1}=1024, r=0.5 $$

Find the 32nd term of each sequence. \(9,4,-1,-6,-11, \ldots\)

Write an explicit formula for each sequence. Then find \(a_{12}\) $$ \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \dots $$